How can I align captions with each level of a tree drawn with tikz-qtree?

Here's the same tree typeset with version 0.05 of the experimental justtrees.sty. (Should you wish to play guinea pig for me, please let me know so I can give you a current version. An earlier version is somewhere on this site.)

Answering this question using justtrees let me to fix one more bug....

---

To add the labels at the right you just say just=<label> for any of the nodes at the appropriate level of the tree. Since the labels have = in them, they need protection with curly brackets in this case.

The bracketing of the groups of nodes is done with a new style bracket me=<end node>. This should be applied to the leftmost node of the group. The argument should be a reference (name or forest relative name or alias etc.) to the rightmost node of the group. I've bracketed 2 such groups just for demonstration purposes here.

documentclass[tikz,border=10pt]{standalone}
usepackage{justtrees}% version 0.05
begin{document}
begin{justtree}
  {
    /tikz/every node/.append style={font=sffamily},
    /tikz/select/.style={font=sffamilybfseries},
    just format={font=sffamilybfseries},
    /forest/bracket me/.style={
      tikz+={draw [thick] (.south west) +(0,5pt) |- (#1.south east) -- +(0,5pt);}
    }
  }
  [0
    [0, just={v=2}
      [0, just={v=4}
        [0, just={v=8}, select, bracket me=4]
        [1, select]
      ]
      [1
        [2, select]
        [3, select]
      ]
    ]
    [1
      [2
        [4, select, name=4]
        [0
          [0, select, bracket me=p]
          [1, select]
        ]
      ]
      [3
        [1
          [2, just={v=5}, select]
          [3, select]
        ]
        [2
          [4, select, name=p]
          [0
            [dots, triangle]
          ]
        ]
      ]
    ]
  ]
end{justtree}
end{document}

Another solution using forest:

  begin{forest}
  label tree,
  for tree={
    circle,draw,
    s sep'=10pt, 
    edge+=thick,  
    font=strutfootnotesizesffamily,
  },
[A, name=lvl0
    [B
      [C, edge label={node[midway,left] {}} ] 
      [D] 
      [E
      [F]
      [G]
      ]
      ]
    [H, name=lvl1 
    [I
      [J]
      [K]
    ] 
      [L] 
      [M, name=lvl2 
      [N, name=lvl3
      ]
      ]
  ] 
]
node[right=4.05cm of lvl0, Comment] {Level 0};
node[right=1.75cm of lvl1, Comment] {Level 1};
node[right=0.6cm of lvl2, Comment] {Level 2};
node[right=0.6cm of lvl3, Comment] {Level 3};
end{forest}

A minimal working code:

documentclass[aspectratio=169,10pt]{beamer}
% documentclass[border=10pt]{standalone}
usepackage{tikz}
usepackage{forest}
forestset{%
  label tree/.style={
    for tree={tier/.option=level},
    level label/.style={
      before typesetting nodes={
        for nodewalk={current,tempcounta/.option=level,group={root,tree breadth-first},ancestors}{if={>OR={level}{tempcounta}}{before drawing tree={label me=##1}}{}},
      }
    },
    before drawing tree={
      tikz+={coordinate (a) at (current bounding box.north);},
    },
  },
  label me/.style={tikz+={node [anchor=base west] at (.parent |- a) {#1};}},
}

usetikzlibrary{arrows.meta, calc, positioning}

tikzset{%
    Comment/.style={%
        draw=none,
        inner sep=0mm,
        outer sep=0mm,
        minimum height=5mm,
        align=right
    },
}


begin{document}
begin{frame}{}
  begin{forest}
  label tree,
  for tree={
    circle,draw,
    s sep'=10pt, 
    edge+=thick,  
    font=strutfootnotesizesffamily,
  },
[A, name=lvl0
    [B
      [C, edge label={node[midway,left] {}} ] 
      [D] 
      [E
      [F]
      [G]
      ]
      ]
    [H, name=lvl1 
    [I
      [J]
      [K]
    ] 
      [L] 
      [M, name=lvl2 
      [N, name=lvl3
      ]
      ]
  ] 
]
node[right=4.05cm of lvl0, Comment] {Level 0};
node[right=1.75cm of lvl1, Comment] {Level 1};
node[right=0.6cm of lvl2, Comment] {Level 2};
node[right=0.6cm of lvl3, Comment] {Level 3};
end{forest}
end{frame}
end{document}

This code will work for both beamer as well as other classes.